Solid layer thermal-conductivity measurement ... - Semantic Scholar

Solid layer thermal-conductivity measurement techniques KE Goodson DaimlerBenz AG, Reseqrch and Technology (FIW/FF), Postfach 2360, 89013 Ulm, Germany

MI Flik Behr GmbH& Co, Postfach 300920, 70449 Stuttgart, Germany The thermal conductivities of solid layers of thicknesses from 0.01 to 100 urn affect the performance and reliability of electronic circuits, laser systems, and microfabricated sensors. This work reviews techniques that measure the effective thermal conductivity along and normal to these layers. Recent measurements using microfabricated experimental structures show the importance of measuring the conductivities of layers that closely resemble those in the application. Several promising non-contact techniques use laser light for heating and infrared detectors for temperature measurements. For transparent layers these methods require optical coatings whose impact on the measurements has not been determined. There is a need for uncertainty analysis in many cases, particularly for those techniques which apply to very thin layers or to layers with very high conductivities.

CONTENTS NOMENCLATURE 1. INTRODUCTION 2. CONDUCTIVITY ALONG LAYERS 2.1 Steady-state techniques 2.2 Transient techniques... 3. CONDUCTIVITY NORMAL TO LAYERS 3.1 Steady-state techniques 3.2 Transient techniques 4. SUMMARY AND RECOMMENDATIONS ACKNOWLEDGMENT REFERENCES BIOGRAPHICAL INFORMATION

K

n,eff

:

101 102 103 103 105 107 107 109 110 110 110 112

"•sub

kT L L0 I Q q lal

NOMENCLATURE qy

C d dgub dj E E" h / KQ k ka,eff *app

= specific heat per unit volume, J m 3 K"1 = layer thickness, m = substrate thickness, m = thickness of thermocouple bridge, m = energy deposited by laser, J = energy deposited per unit area, J nr 2 = heat transfer coefficient, W nr 2 K~1 = integer in summation, Eq (11) = modified Bessel function of first kind of order zero = thermal conductivity, W nr 1 K"1 = effective thermal conductivity for conduction along layer, W nr 1 K"1 = apparent thermal conductivity measured by thermal comparator, W nr 1 K"1

R-app R-sub Rf

r rc T AT Ta TA TB

T{ To Ti t tL

UT

= effective thermal conductivity for conduction normal to layer, W nr 1 K"1 = substrate thermal conductivity, W nr 1 Kr1 = thermocouple bridge thermal conductivity, W nr 1 K-1 = length, m = Lorenz number = 2.45 x 10~8 W H K~2 = half-width of laser line, m = heat flow, W = heat flux, W nr 2 = amplitude of periodic heat flux, W nr 2 = heat-flow amplitude per unit length, W n r l n = heat flux in x direction, along layer, W nr 2 = heat flux in y direction, normal to layer, W m 2 = apparent thermal resistance, m2 K W"1 = substrate thermal resistance, m2 K W"1 = thermal resistance, m2 K W"1 = distance from heating source, m = heat-flow radius, m = temperature, K = temperature difference, K = amplitude of periodic temperature, K = temperature of bridge A, K = average substrate temperature below bridge A, K = initial layer temperature due to pulse heating, K = boundary or reference temperature, K = boundary temperature, K = time, s = duration of laser pulse, s = ratio of temperature changes

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101

© 1994 American Society of Mechanical Engineers

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102

w x xs y

Goodson and Flik: Thermal-conductivity measurement techniqi

= width, m = coordinate in plane of substrate, m = separation between bridges, m = coordinate normal to substrate, m

Greek Symbols a = thermal diffusivity, m 2 s"1 e = emissivity Ax = inverse thermal diffusion length = (to/cc)1/2, nr 1 pe = electrical resistivity, Q, m CO = angular frequency, rad s"1

1.

INTRODUCTION

The thermal conductivities of thin solid layers are needed for the design of field-effect transistors in electronic circuits, coated lenses in laser systems, and microfabricated superconducting radiation detectors (Goodson and Flik, 1992; Guenther and Mclver, 1988; Verghese et al, 1992). The thermal conductivity of a layer can differ from that of a bulk sample of the same material for two reasons. Layer fabrication techniques, such as chemical-vapor deposition (CVD), usually result in a microstructure or purity in the layer that differs from that in the bulk material, which influences the thermal conductivity. In addition, the small thickness of the layer can increase the importance of interfacial effects such as thermal boundary resistances and the boundary scattering of heat carriers, electrons and phonons. This can reduce the effective conductivity of the layer. Transmission electron microscopy, micro-Raman spectroscopy, and x-ray and electron diffraction provide insight into the microstructure of layers. But the precise microstructural information, e.g., the size and orientation of grains and the density of point defects, needed for predictions of the thermal conductivity is often not available. This makes accurate techniques for measuring the conductivity of layers essential. Cahill et al (1989) reviewed several techniques which measure the thermal conductivity in the direction normal to layers. These authors made helpful observations about the effects of phonon-boundary scattering and interfacial layers on the measurements at cryogenic temperatures. Some of these insights are presented in greater detail in the review of research on thermal boundary resistance by Swartz and Pohl (1989). Graebner (1993) described techniques that measured the thermal conductivity of CVD diamond layers and compared the resulting data. There remains a need for a review which includes techniques used for other layers, especially the thin, low-conductivity amorphous layers that coat lenses and serve as passivation in circuits. Guenther and Mclver (1988) and Lambropoulos et al (1991) surveyed the existing data for the thermal conductivity in the direction normal to amorphous dielectric layers, but in most cases did not provide the details of the measurement techniques used to obtain these data. As a result, it is often difficult to assess the accuracy of the techniques or their applicability to layers

Appl Mech Rev vol 47, no 3, March 1994

which have different thicknesses or are made of different materials. This work helps to remedy this situation by reviewing layer thermal-conductivity measurement techniques. The layer geometry is depicted in Fig 1, which defines the coordinates x and y to be along and normal to the layer, respectively. The thermal conductivity measured in layers is not necessarily a property of the layer material. Due to heatcarrier boundary scattering or thermal boundary resistances, the apparent thermal conductivities of layers often depend on the direction of heat flow, even for isotropic materials, the layer thickness, and the properties of the layer boundaries. For this reason, most measurements yield an effective thermal conductivity, which is valid only for a given layer thickness and direction of heat flow. The effective thermal conductivity along a layer is

W = -ft [J]"

(1)

where T is the local layer temperature, which is assumed not to vary in the y direction, and effoi diamond layers. The substrate is etched from beneath the rectangular layer section shown.

105

qa 2 CO C d

exp

x V2"

KT

(5)


106

Goodson and Flik: Thermal-conductivity measurement techniques 1/2

The inverse thermal-diffusion length is Ax = (co/a) , where a is the thermal diffusivity in the x direction. The distance between the thermocouple and the mask edge can be changed by moving the mask. Equation (5) and the measured function Ta{x) yield a. The frequency must be small enough so that the thermal diffusion length is much larger than the layer thickness. Subsequent research investigated the influence of the thermocouple on the temperature in the layer (Hatta et al, 1986) and optimized the sample dimensions for the measurement (Hatta et al, 1987). The authors did not investigate the potential of a microfabricated thermocouple, such as those employed by Graebner et al (1992c), for measuring temperature without disturbing conduction in the layer. Similar techniques developed by Visser et al (1992) and Shibata et al (1991) avoided the influence of the thermocouple on conduction in the layer by using infrared thermography to measure the layer temperature. Visser et al (1992) used a highly-focussed, periodic laser beam to heat a spot with diameter near 10 jim on a layer of large dimensions. A solution to the transient one-dimensional thermal-conduction equation with cylindrical coordinates yields the phase and amplitude of the periodic temperature in the layer as functions of its diffusivity a, heat capacity per unit volume C, the distance from the focus, and the heat transfer coefficient h from the layer surface to the ambient temperature. Fitting the measured amplitude and phase of the temperature fluctuations to the predictions yields a and h. In the techniques of Hatta (1985) and Visser et al (1992), the phase of the temperature fluctuations yields the thermal diffusivity without requiring the heat transfer coefficient h. The primary advantage of the technique of Visser et al (1992) is that it does not require physical contact with the sample layer. The method of Hatta (1985) could also be applied using infrared thermography. Shibata et al (1991) employed a brief line pulse of laser light of time duration tL and spatial width 21 to irradiate a free-standing rectangular layer section. The line was incident

PERIODIC RADIATION FLUX, ANGULAR FREQUENCY (0 I I I I I I

I

I

I

I

? ? ? ? ? J

¥

¥

¥

7

MOVABLE MASK

r

¥

SAMPLE LAYER BRIDGE

THERMOCOUPLE LEADS

FIG 5. Side view of the experimental structure of Hatta (1985) for measuring the thermal diffusivity along layers heated by a sheet of laser light. The mask was moved to change the distance x while the thermocouple junction remained fixed.

Appl Mech Rev vol 47, no 3, March 1994

on the entire width w of the layer section at its center, inducing one-dimensional heat conduction along its length. The half-width / and the time duration ti of the laser-pulse line satisfied fi > > a tj. This allowed the transient temperature in the layer to be calculated by assuming an initial temperature change Tj - TQ = E / (21 d w C) in the irradiated portion of the layer, where E is the total energy deposited. Heat transfer from the layer was neglected. The temperature was detected from the bottom of the layer at a distance from the heat source which was large compared to the layer thickness. Comparison of the time required for the measured temperature to reach half of its maximum value with the analytical prediction of this time yielded the thermal diffusivity. The impact of neglecting heat-transfer from the layer needs to be assessed. Photo thermal displacement spectroscopy at transient thermal gratings is based on the principle of Eichler et al (1971; 1973), who used the interference of two pulsed laser beams at the same frequency with different angles of incidence on a sample to deposit energy with a density that varied periodically in one lateral dimension. The technique of Harata et al (1990) and Kading (1993a) generates heat at the surface of the sample layer. The thermal expansion of the layer due to the brief laser pulse results in a spatiallyperiodic displacement of the surface, whose exponential decay with time is governed by the lateral thermal diffusivity of the layer within a depth comparable to the spatial period of the grating. The time dependence of the deflection of a probe laser beam yields the relaxation time of the displacement, from which the diffusivity is calculated. The depth of observation in the sample can be controlled by varying the spatial period of the grating. Kading et al (1993a; 1993b) provided theory for this method that facilitated diffusivity measurements in CVD diamond layers within a depth as small as 10 jam. This method has the advantage of being local in three dimensions with a lengthscale comparable to the grating period. The uncertainty of data obtained using this technique must be determined, particularly for measurements on layers of very high thermal diffusivity. The optical techniques require the deposition of a thin absorbing coating on transparent or semi-transparent layers. If these coatings are too thick, they influence the diffusivity measurement. For coatings of low thermal diffusivity, the heat cannot diffuse through the coating during the relevant time interval, e.g., one period of the laser flux. This problem can be aggravated by a thermal resistance between the coating and the layer. If the diffusivity of the coating is too high, it may contribute to transport in the plane of the layer. Visser et al (1992) compared values of the thermal diffusivity of measured in copper sheets of thickness 100 urn that were coated with different materials. Their data show that the coating material can strongly influence the measured diffusivity. The influence of the coating material on the diffusivity measurement increases with decreasing layer thickness. Further investigation needs to determine the appropriateness of optical techniques for measuring the


Appl Mech Rev vol 47, no 1, Part 1, January 1994 thermal diffusivity absorbtances. 3. 3.1

of

very-thin

layers

Nguyen: Bifurcation and stability in dissipative media with

low

R UT =

The techniques described in this sub-section apply only to layers on substrates satisfying kn>eff K< ksl,b. Goldsmid et al (1983) developed a technique to measure the thermal conductivity of an amorphous silicon layer, which was deposited on half of a substrate as shown in Fig 6. Two bismuth bridges were deposited, one each on the layer and the bare substrate. An antimony bridge was deposited over the two bismuth bridges as shown, yielding two thermocouples. The portion of the sample in the dashed rectangle in Fig 6 was coated to enhance radiation absorption. The thermocouple junctions were heated sequentially using a disc of laser light with radius rc = 55 |im. For each case, all of the laser light was incident on the junction. The temperature rise due to the laser light was measured for each case. The ratio of the temperature rise of the thermocouple above the sample layer and the temperature rise of the thermocouple above the bare substrate is UT, The substrate was modelled as a semi-infinite medium with thermal resistance Rsub = (jil$)(rclksub), corresponding to heat flow in a semi-infinite medium originating from an isothermal disc of radius rc. The thermal resistance of the sample layer is d/kneff, and the thermal resistance between the thermocouple junction and the sample surface is dj/kj, where Jj-and k-j-are the thickness and thermal conductivity of the bismuth layer, respectively. The effective layer thermal conductivity klheff can be determined by equating the ratio of the temperature changes to the ratio of the summed resistances,

FIG 6. Top view of the experimental structure of Goldsmid et al (1983) for measuring kn,eff

+ eg.

Appl Mech Revvol 47, no 3, March 1994

These assumptions are important because Brotzen et al (1992) reported values of k,hejj which are much smaller than those measured in bulk samples. It is not yet possible to determine whether this difference was due to a different layer property or to the approximations in the thermal-conduction analysis. The technique of Cahill et al (1989) is more accurate than those of Schafft et al (1989) and Brotzen et al (1992) because the temperature under the sample layer is calculated using the substrate temperature measured nearby. As a result, klhejf is less sensitive to approximations in the thermal analysis. Lambropoulos et al (1989) modified the thermal comparator technique, which was developed by Powell (1957) to measure the thermal conductivity of bulk materials, to measure kn>eff for layers on substrates. A sensing finger and thermocouple apparatus were mounted in a copper heating block as shown in Fig 8. One junction of the thermocouple was at the tip of the finger while the other was inside the block. The temperatures of the copper block and the sample were maintained at 329 and 309 K, respectively. During the measurements, the finger was pressed against the sample with a controlled force and the steady-state thermocouple voltage was recorded. The samples were assumed to be well modelled as semi-infinite media. The temperature of the sensing tip decreased and the thermocouple voltage increased with the increasing thermal conductivities of the sample materials. Measurements performed on bulk samples with known thermal conductivities yielded a calibration curve from which the apparent thermal conductivity of a sample, kapp, could be obtained from the thermocouple voltage. For a layer on a substrate, kneffcan be calculated by assuming the thermal resistance of the substrate is Rsub = (7r/4)(rc/^HZ)), the relation used by Goldsmid (1983). The difference between Rsub and the apparent resistance Rapp = (is/4)(rclkapp) is due to the layer resistance dlkneff, yielding

W-4rf/_L- . _l_\l 71 r

eff If the thermal conductivity is anisotropic, the radial symmetry of the technique yields a conductivity which is a function of the thermal conductivities both normal to and along the layer. The measured conductivity is most affected by regions near the surface of the layer. As a result, the thermal conductivity obtained using the 3-co method may not be appropriate for analyzing steady-state conduction normal to thin-layered structures. The influence of thermal boundary resistances on this technique has not been assessed. These could be important, particularly at low temperatures. The second type of transient technique for measuring the thermal conductivity normal to layers is non-contact and applies to free-standing layers. A brief pulse of laser energy is applied at the layer surface, and the thermal conductivity is calculated from the transient temperature of the opposite layer surface, measured using IR thermography. This approach was recently applied to amorphous polymer layers by Tsutsumi and Kiyotsukuri (1988), to metals by Shibata et al (1991), and to diamond layers by Graebner et al (1992b). Like the optical techniques discussed in Section 2.2, this one benefits from the deposition of opticallyabsorbing layers on the front and rear surfaces. The thermal resistances and heat capacities per unit area of these layers can be made small compared to those of the sample layer. For a sheet of laser light incident on one surface of the layer, the analysis of one-dimensional conduction through the layer yields the approximate temperature rise at the opposite side at time t after the energy deposition (Graebner et al, 1992b),

AT{t)=ML l Cd

+

2^(-l)"exp(:ifjdaf)

Pompe and Schmidt (1973). The application of these optical methods to very thin layers requires additional research on the impact of absorbing coatings. Tai et al (1988), and Mastrangelo and Muller (1988) and VolHein and Baltes (1992) developed novel microstructures for thermal conductivity measurements that closely resembled the structure whose design required the property. Techniques measuring the effective thermal conductivity normal to layers are summarized in Table II. Goldsmid (1983) developed a useful technique whose uncertainty needs further investigation. The technique of Cahill et al (1989) is the most accurate because it comes the closest to measuring the temperature on both sides of the sample layer. The technique of Lambropoulos et al (1989), which employs a thermal comparator, is an easily-applied nondestructive technique, but requires more work to precisely determine the contact area. The 3-co technique of Cahill et al (1989) allows a targeted depth within the layer to be probed, but is limited to layers thicker than about 10 jum. More detailed uncertainty analysis is required for most of the techniques available. Uncertainty analysis is made more important by the large heat fluxes present in thin layers in microelectronic circuits. A relatively small error in the measured conductivity of a layer can cause a large absolute temperature error, resulting in inaccurate predictions of the circuit performance and reliability. The microstructures of thin layers depend strongly on the fabrication techniques used to make them. Thermal conductivity measurements must therefore be performed using microstructures fabricated using the same processes as those of the real devices for which the thermal conductivity is needed.

(11)

where a is the thermal diffusivity in the direction normal to the layer, E" is the energy deposited per unit area and C is the specific heat per unit volume. Fitting the measured response of the detector to Eq (11) yields a. Both the period of the pump laser and the response time of the detector need to be much smaller than d2 I a. This limits the practical application of this technique relatively thick layers. For 5 um amorphous layers at room temperature, d2 I a is of the order of 25 us, which requires a rather fast IR detector. For highly-conductive layers, such as silicon and diamond, the application of this technique is limited to layers several tens of micrometers thick. The possibility of using an electrical-resistance thermometer bridge, deposited on the back surface of the layer, should be investigated. This would decrease the response time and allow thinner layers to be measured. 4.

AppI Mech Rev vol 47, no 3, March 1994

SUMMARY AND RECOMMENDATIONS

The techniques measuring the thermal conductivity along layers are summarized in Table I. The periodic optical techniques of Harata et al (1990), Kading et al (1993a; 1993b), Hatta (1985), and Visser et al (1992) provide attractive alternatives to the standard steady-state technique of

ACKNOWLEDGMENT K.E.G. was supported by the Office through an academic fellowship.

of Naval Research

REFERENCES Boiko BT, Pugachev AT, and Bratsychin VM (1973), Method for the Determination of the Thermophysical Properties of Evaporated Thin Films, Thin Solid Films 17 157-161. Brotzen FR, Loos PJ, and Brady DP (1992), Thermal Conductivity of Thin SiC>2 Films," Thin Solid Films 207 197-201. Cahill DG (1990), Thermal Conductivity Measurement from 30 to 750 K: The 3w Method, Rev Sci Inst 61 802-808. Cahill DG, Fischer HE, Klitsner T, Swartz ET, and Pohl RO (1989), Thermal Conductivity of Thin Films: Measurements and Understanding, J Vac Sci Technol A7 1259-1266. Cahill DG, and Pohl RO (1987), Thermal Conductivity of Amorphous Solids above the Plateau, Phys Rev B 35 4067-4073. Carslaw HS, and Jaeger JC (1959), Conduction of Heat in Solids, Oxford UP, New York. Dua AK, and Agarwala RP (1972), Thermal Conductivity of Thin Films of Alkali Metals, Thin Solid Films 10 137-139. Eichler H, Enterlein G, Munschau J, and Stahl H (1971), Lichtinduzierte, Thermische Phasengitter in Absorbierenden Fliissigkeiten, Zeitschrift fur Angewandte Physik, 31 1-4. Eichler H, Salje G, and Stahl H (1973), Thermal Diffusion Measurements using Spatially Periodic Temperature Distributions induced by Laser Light, / Appl Phys 44 5383-5388. Goldsmid HJ, Kaila MM, and Paul GL (1983), Thermal Conductivity of Amorphous Silicon, Phys Stat Sol 76, K31-K33.


Appl Mech Rev vol 47, no 1, Part 1, January 1994

Nguyen: Bifurcation and stability in dissipative media

111

Table I. Summary of techniques measuring the effective thermal conductivity along layers. Geometry

free-standing bridge free-standing electrically conducting bridge

Tested Temp. Range 10450 K 80700 K

substrate etched from beneath portion of layer free-standing bridge free-standing bridge free-standing layer layer with or without substrate

near 300 K near 300 K near 300 K near 300 K near 300 K

Heating Time-Dependence and Source steady-state heater

Temperature Measurement

References

thermocouple

steady-state or transient Joule heating

sample-bridge electrical resistance

steady-state heater-bridge periodic laser sheet incident on half of bridge laser pulse, line focus

microfabricated thermocouples thermocouple

Nath and Chopra (1973); Morelli et al (1988) Volklein and Kessler (1984); Mastrangelo and Muller (1988); Boiko et al (1973); Tai et al (1988) Graebner et al (1992c)

periodic laser beam with point focus two pulsed laser beams that interfere on surface

Hatta (1985)

IR thermography

Shibata et al (1991)

IR thermography

Visser et al (1992)

deflection of probe laser beam

Harataet al (1990); Kadinget al (1993a)

Table II. Summary of techniques measuring the effective thermal conductivity normal to layers. Layer Geometry

dielectric layer on substrate dielectric layer on substrate dielectric layer on substrate layer on substrate layer with or without substrate dielectric layer with or without substrate free-standing layer

Temperature References Tested Heating Measurement Temp. Time-Dependence Range and Source thermocouple Goldsmidet al(1983) near steady-state laser bridges 300 K with disc-shaped focus Cahill et al (1989); Schafft et al bridge resistance 10steady-state heating in thermometers (1989);Goodsonet al (1993a; 1993b) 400 K microfabricated bridge thermocouple Brotzenet al(1992) near steady-state heating on heater 300 K in microfabricated bridge thermocouple Lambropoulos et al(1989) near steady-state heating in 300 K copper block Nonnenmacher and near steady-state heating through contact potential at AFM probe tip Wickramsinghe (1992) 300 K AFM probe tip bridge resistance Cahillet al (1989) 1periodic heating in a thermometer 300 K microfabricated bridge IR thermography Graebner et al (1992b); near pulsed sheet Shibata et al (1991); Tsutsumi and 300 K of laser light Kiyotsukuri (1988)

Goodson KE, and Flik MI (1992), Effect of Microscale Thermal Conduction on the Packing limit of Silicon-on-Insulator Electronic Devices, IEEE Trans. Components, Hybrids, and Manufacturing Technology 15 715-722. Goodson KE, Flik MI, SuLT, and Antoniadis DA (1993a), Prediction and Measurement of the Thermal Conductivity of Amorphous Dielectric Layers, J Heat Transfer, in press. Goodson KE, Flik MI, Su LT, and Antoniadis DA (1993b), AnnealingTemperature Dependence of the Thermal Conductivity of LPCVD Silicon-Dioxide Layers, IEEE Electron Device Letters 14 490-492. Goodson KE, Flik MI, Su LT, and Antoniadis DA (1993c), Prediction and Measurement of Temperature Fields in Silicon-on-Insulator Electronic Circuits, in Solutions to CFD Benchmark Problems in Electronic

Packaging, ASME HTD-Vol. 255, D Agonafer (ed), 11-19. Submitted to ASME J Heat Transfer. Graebner JE (1993), Thermal Conductivity of CVD Diamond: Techniques and Results, Diamond Films and Technology 3 77-130. Graebner JE, Jin S, Kammlott GW, Herb JA, and Gardinier CF (1992a), Unusually High Thermal Conductivity in Diamond Films, Appl Phys Lett 60 1576-1578. Graebner JE, Jin S, Kammlott GW, Bacon B, Seibles L, Banholzer W (1992b), Anisotropic Thermal Conductivity in Chemical Vapor Deposition Diamond, / Appl Phys 71 5353-5356. Graebner JE, Mucha JA, Seibles L, and Kammlott GW (1992c), The Thermal Conductivity of Chemical-Vapor-Deposited Diamond Films on Silicon, J Appl Phys 71 3143-3146.


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Goodson and Flik: Thennal-conductivity measurement techniques

Guenther AH, and Melva JK (19118), The Role of Thcnllal Conductivity in the Pulsed Laser Damage Sensitivity of Optical Thin Films, Thin Solid Films 163 203-214. Harata A, Nishimura H, and Sawada T (1990), Laser-Induced Surface Acoustic Waves and PhotothemJal Surf.1ce Gratings Generated by Crossing Two Pulsed Laser Beams, Appl Phys Leu 57 132-134. . Hatla I (I9RS), Thennal Diffusivity Measurement of Thin Films by Means of an AC Calorimetric Method, Rev Sci Instl'llm 56 1643-1646. Hatla I, Kato R, and Maesono A (1986), Development of AC Calorimetric Method for Thermal Diffusivity Measurement. I, Contribution of Thermocouple Attachment in a Thin Sample, Ipn J Appl Phys 25 L493-lA95. Halla I, Kato R, and Maesono A (1987), Development of AC Calorimetric Method for Thermal Diffusivity Measurement. n. Sample Dimension Required for the Measurement, Ipn 1 Appl Phys 26 475-478. Kiiding OW, Matthias E, Zachai R, Fiiller H-J, and Miinziger P (l993a), Thermal Diffusivities ofll1in Diamond Films on Silicon, Diamond and Related Materials 21185-1190. Kading OW, RosIer M, Zachai R, and EiBer H-J, (I 993b), Lateral Thermal Diffusivity of Epitaxial Diamond Films, Diamond and Related Materials, in press. Kittel C (1986), Introduction to Solid State Physics, Wiley, New York, 150-153. Lambropoulos JC, Jacobs SD, Burns SJ, Shaw-Klein L, and Hwang SS (1991), Thermal Conductivity of Thin Films: Measurement and Microstmctural Effects, in Thin Film Heat Tl'all.~ter - Pmperties and Pmcessing, ASME HTO-Vol. 184, MK Alam et al (eds), 21 -32. Lambropoulos IC, Jolly MR, Amsden CA, Gilman SE, Sinicropi MJ, Diakomihalis D, and Jacobs SD (1989), Thcrmal Conductivity of Dielectric Thin Films, 1 Appl Phys 66 4230-4242. Mastrangelo CR, and Muller RS (1988), Theronl Diffusivity of Heavily Doped Low Pressure Chemical Vapor Deposited Polycrystalline Silicon Films, Sensors alld Materials 3, 133-141. Morelli DT, Beetz CP, and Perry TA (1988), "Thernlal Conductivity of Synthetic Diamond Films," J Appl Phys 643063-3066. Nath P, and Chopra KL (1973), Experimental Determination of the Thermal Conductivity ofThin Films, Thin Solid Fiblls 18 29-37. Nonnemnacher M, O'Boyle MP, and Wickramsinghe HK. (1991), Kelvin Probe Force Microscopy, AppJ Ph)'s utt 58 2921-2923.

Appl Mech Rev vol 47, no 3, March 1994 Nonnenmacher M, and Wickramsinghe HK (1992), Scanning Probe . Microscopy ofThermal Conductivity and Subsurface Propcrties, Appl Phys Lett 61 168-170. Pompe G, and Schmidt K (1975), Vapour-Deposited Lead Films and Their Transport Characteristics at Low Tempcratures, Phys SIal Sol A31, 37-46 . Powell RW (1957), Experiments Using a Simple Thermal Comparator for Measurement of Thermal Conductivity, Surface Roughness and Thickness of Foils or of Surface Deposits, 1 Sci Illstrulll 34485-492. Schafft HA, Suehle JS, and Min:l PGA (1989), Thermal Conductivity Measuremcnts of Thin-Film Silicon Dioxide, in Proceedings of tlte IEEE IIIte11lationai COllference 011 Micl'OelectJ'ollic Test Struclllres, AJ Walton et al (eds), Edinburgh, Scotland, March 13-14,2 121-124. Shibala H, Ohta H, Wascda Y (1991), New Laser Flash Method for Measuring Thermal Diffusivity of Isotropic and Anisotropic Thin Films, 11M Mal Trans:n 837-844. Siegcl R, and Howell JR (1981), Thenl/al Radiation Heat Transfer, Hemisphere, New York, 111-117. Swartz ET, and Pohl RO (1987), Thermal Resistance at Interfaces, Appl Phys Lett 51 2200-2202. Swartz ET, and Pohl RO (1989), Thermal Boundary Resistance, Rev Mod Pltys 61 605-668. Tai YC, Mastrangelo CH, and Muller RS (1988), l1termal Conductivity of Heavily Doped Low-Pressure Chemical Vapor Deposited Polycry,talline Silicon Films, 1 Appl Phys 631442-1447. Tsutsumi N, and Kiyotsukuri T (1988), Measurement of Thermal Difthsivity for Polymer Film by Flash Radiometry, Appl Phys Lett 52 442-444. Verghese S, Richards PL, Char K, Fork OK, and Geballe TH (1992), Feasibility of Imaging Arrays Using High-Tc Snperconducting Bolometers, 1 Appl Pltys 71 2491-2496. Visser EP, Versteegen EH, Enckevort Jp (1992), Measurement of Thennal Diffusion in Thin Films Using a Modulated Laser Technique: Application to Chemical-Vapor-Deposited Diamond Films, 1 Appl Phys 71 3238-3248. VOlklein F, and Baltes H (1992), A Microstructure for Measurement of Thennal Conductivity of Polysilicon Thin Films, J Microeleclrolllechanical Systems 1 193-196. Volklein F, and Kessler E (1984), A Method for the Measurement of Thennal Conductivity, Thermal Diffusivity, and Other Transport Coefficients of Thin Films, Phys Stat Sol AS1 585-596.

Kenneth E Goodson received the BS, MS, and PhD degrees in mechanical engineeringji'Oln the Massachusetts Institute of Technology in 1989, 1991, and 1993, respectively, He has been a visiting scientist at the research center ofDaimler Benz AG in Ulm, Germany since Spring, 1993, In Fall. 1994, he willjoin the Mechanical Engineering Department at Stanford University as an assistant prOfessor. His research interests include thermal conduction in layers ofCVD diamond, am01phous dielectrics, and high-Tc superconductors, and in electronic devices, ego IMPATT diodes andfield-eiJect transistors. At Daimler Benz, he is helping to develop high- . power electronic systems containing CVD diamond for applications in vehicles. He received a graduate fellowship ji-om the Office ofNaval Research and belongs to the Tau Beta Phi, Phi Beta Kappa, and Sigma Xi honor societies. Markus I Flik received the Dipl Ing degreeji-om the Swiss Federal Institute 0/ Technology, Zurich, in 1985, and the MS and PhD degrees in mechanical engineeringjrom the University of California, Berkeley, in 1987 and 1989, respectively. He was with the Department ofMechanical Engineering at the Massachusetts Institute ofTechnology as an assistant professorji-om July 1989 to June 1992 and as an associate professorfrom July 1992 to August 1993. At present, he is director ofstrategic planning at Behr, GmbH & Co, a major supplier afvehicle thermal management systems based in Stuttgart, Germany. His research interests include thermal radiation and conduction in microstructures, eg, thin films and multiple quantum wells, and in novel materials, eg high-Tc superconductors and CVD diamond. He held the HatlY and Lynde Bradley Foundation and the Samuel C Collins Career Chairs during his period at MIT. He received the Silver Medalfrom the Swiss Federal Institute ofTechnology.
